Study of Combustion pattern in Oblique Detonation Engine

Oblique detonation engines are being a centre of multiple kinds of research. Likewise, this paper provides the simulation at various Mach numbers to observe the pattern of combustion in an oblique detonation engine. considering Rahul et al paper[5] as a reference same conditions of pressure, temperature and wedge angles were used in this paper. yet, a different model of a chemical designed by M.O Conaire and H.J Curran[7] was used and simulation was performed at several Mach numbers until a fully developed combustion had been achieved.


Introduction
Over the years, researchers have been studying the ways of making propulsion more efficient. Oblique detonation wave engines are one among them where detonation plays a key role. It is a mode of combustion which propagate supersonically and it is highly preferred due to its better thermodynamic cycle efficiency than constant pressure cycle or constant volume cycle. This makes detonation highly suitable for the supersonic and hypersonic propulsion system. Looking back into the researches provided in David etal [1] paper, Roy [2] introduced the concept of stabilized normal detonation wave(NDW) in 1946 for hypersonic aircraft. However, to stabilize NDW in steady flow it required variable engine geometry. Then, normal detonation meaning flow downstream would be sonic or subsonic which in turn results in high static temperature which can be the reason for the dissociation of combustion products. NDW could not be suggested beyond Mach number 6 as performance falls steeply. Ferri [3] suggested the use of deflagration or diffusive combustion to preserve the supersonic flow in the combustor so this new concept was preferred more than NDW since then. Next, Dunlap et al [4] came up with the use of stabilized oblique detonation wave for hypersonic ramjet propulsion. According to Dunlap, the only normal component of flow leaving an ODW is sonic or subsonic. Hence, supersonic flow can be preserved throughout the combustor. It is of great importance because If the incoming Mach number is less as compared to Chapman-Jouguet Mach number, an unsteady normal detonation wave is experienced in the combustor. On the other hand, exceeding incoming Mach number as compared to CJ Mach number will lead to oblique detonation. Further, to stabilize wave variable geometry is not required as it is done solely by a wedge. Not only this, but ODWEs are also more advantageous than SCRAMJET engines owing to the fact that it gives short combustor length and less inlet diffusion. Moreover, these engines can help in delaying the rocket operation because of their performing abilities and the amount of oxygen carried on board could be decreased too. There were experimental attempts made between the 1950s to 1960s but were limited and got the speed only after the Sputnik project in national aerospace research. Since then this has become a vital topic of research. So, this paper is also an effort to study the combustion in ODWE considering Rahul Kumar, AjjayOmprakas and Donald R Wilson [5]paper as a reference. They had provided a detailed analysis of oblique detonation wave using ANSYS Fluent. They used the hydrogen-air mixture,9 species and 28 steps, chemical reaction model [6], at a specific Mach number 6 and wedge angle 20ᵒ respectively. The same air-fuel mixture has been used in the current study with a different chemical model designed by M.O Conaire and H.J Curran (11 species and 19 steps chemical reactions) [7]. The wedge angle is taken 20ᵒ from the reference paper but with different Mach numbers to obtain the pattern of combustion using ANSYS Fluent.

Computational Fluid Dynamics
As mentioned earlier, the area of focus of this paper will be the pattern of combustion inside the combustor. Let's zoom into that area and take it as a 2D model(shown into figure 1), an asymmetric channel having a wedge(transition of geometry at the combustor inlet is said to be a wedge for the simplicity of the analysis). The flow enters from the inlet and collides with the wedge. At this point, oblique shocks are generated and chemical reactions take place due to the high enthalpy of oblique shocks at the wedge. The figure shows the domain of fluid flow where left is combustor inlet and right is the way of exit of combustor towards the nozzle. The conditions such as P1 and T1 were taken from their paper exactly the same, 101325 Pa and 700K respectively. an incoming flow is the premixed hydrogen-air mixture and supersonic flow. At the outlet boundary, the non-reflective boundary condition is imposed. Surface and symmetry plane have slip conditions. Structure grid with different grid spacing is used to mesh various parts of the geometry.

Theory and Calculation
To ease the analysis, geometry is considered to be symmetrical and 2D. Further, Euler equations are applied considering the flow to be inviscid, non-heat-conducting and reacting gas flow which will help in getting a stable oblique detonation wave. Cartesian form of these equations is described as follows 1-4 equations.
Where F and G-convective fluxes, S-Source term vectors Subscript s=1,2,3...Ns (Ns-number of species) Species continuity is represented by the First Ns rows. Next, two rows are of momentum equations. u and v are velocity components in x and y directions respectively. ρ=∑ =1 mixture, shows species density. E-total energy per unit mass, Rs-net rate of production of species of chemical reactions.
Governing equations of continuity, momentum, energy and species transport ANSYS Fluent's set up, density-based solver with the implicit formulation. Advection Upstream Splitting Method(AUSM)(second-order) was applied to get the flux vectors. This method is chosen in order to get the absolute resolution of contact and shock discontinuities because it is oscillations free at stationary and moving shocks. Second-order Upwind scheme with Green Gauss Cell-based method was used for spatial discretization.

Chemical kinetics
The combustion phenomenon is modeled using finite rate chemistry model. It uses Arrhenius expressions to calculate the chemical source. To calculate Rs following equation can be used. where -species s Arrhenius expression can be used to calculate Forward rate constant. , = − ……..8 Here, represents the pre-exponential factor is for temperature exponent (J/Kmol) represents activation energy for the reaction R(J/Kmol-K) is the universal gas constant.
-equilibrium constant of r th reaction.
ANSYS Fluent's function mixing law was employed in getting the mixture specific heat at constant pressure. Every species could be said a function of temperature. In this case, M.O Conaire and H.J Curran [7] hydrogen-air combustion mechanism of 5 species N 2 ,O 2 ,H 2 ,H 2 o and OH and 2 reactions is applied. This technique was chosen due to its accurate global results with fewer reaction steps. In the chemical reactions, N2 is not involved as the highest temperature is still not equal to the dissociation temperature of nitrogen. Nevertheless, it exists as a collision partner.

Mesh Convergence
In order to obtain an optimal design mesh convergence test was performed on sizes 10 -05 m and 8 * 10 -06 m. Mesh convergence was done on the geometry shown above in fig 1. Below fig 3 and 4 conveys the mesh convergence graph at 10 -05 m and 8 * 10 -06 respectively . It can be seen that results do not change on the stated values which proves them to be optimal values. Then, 10 -05 m mesh size is considered in all the further works in this paper.

Results and Discussion
The starting point for this simulation was chosen to be Mach 4 and it is performed for various Mach numbers to observe the pattern of combustion and till proper combustion is achieved in the combustion chamber. Images of pressure, temperature and H 2 O mass fraction at Mach numbers are provided below to understand clearly.Inlet mole fractions of N 2 ,O 2 ,H 2 are 0.556, 0.148 and 0.296 respectively.

Mach 4
Oblique shock is generated at the entry of combustor but seeing H2o figure it is clear combustion is happening somewhere at the extreme left.

Acknowledgements
Not applicable